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Factor the quadratic equation below. 9r^2-5r-10 9r(r-3)(r+2) 9r(r+3)(r+2) r(r-3)(r+2) Cannot be factored

Pergunta

Factor the quadratic equation below.
9r^2-5r-10
9r(r-3)(r+2)
9r(r+3)(r+2)
r(r-3)(r+2)
Cannot be factored

Factor the quadratic equation below. 9r^2-5r-10 9r(r-3)(r+2) 9r(r+3)(r+2) r(r-3)(r+2) Cannot be factored

Solução

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NunoProfissional · Tutor por 6 anos

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To factor the quadratic equation 9r^2 - 5r - 10, we need to find two binomials that multiply together to give us the original quadratic expression.

First, let's rewrite the quadratic equation in standard form:
9r^2 - 5r - 10

We are looking for two numbers that multiply to 9 \times -10 = -90 and add up to -5.

The pair of numbers that satisfy these conditions are 9 and -10, because:
9 \times (-10) = -90
9 + (-10) = -1

However, we need the sum to be -5, not -1. So, we need to find another pair of factors.

After checking possible pairs, we find that:
10 \times (-9) = -90
10 + (-9) = 1

This still doesn't give us the correct sum. Let's try another approach using the quadratic formula to find the roots and then factorize.

The quadratic formula is given by:
r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

For the quadratic equation 9r^2 - 5r - 10, a = 9, b = -5, and c = -10.

Plugging in these values:
r = \frac{-(-5) \pm \sqrt{(-5)^2 - 4 \cdot 9 \cdot (-10)}}{2 \cdot 9}
r = \frac{5 \pm \sqrt{25 + 360}}{18}
r = \frac{5 \pm \sqrt{385}}{18}

Since the discriminant (\sqrt{385}) is not a perfect square, the quadratic does not factor neatly into rational binomials.

Therefore, the correct answer is:
\boxed{\text{Cannot be factored}}
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